I'm confused by this proof and I don't buy it, especially since the definitions, including that of "parsing," are too imprecise to warrant some reduction proof. You also don't need reduction to show the existence of an example, which is what you're essentially trying to do. You seem to be making the claim that when you have code

In a series of three articles in The Perl Review, now available online, I laid this proof out much more carefully, in three different versions. The most bullet-proof version derives the result directly from Rice's Theorem.

You are right that the proof would not go through if the only way of establishing a prototype for a Perl function was via a function definition. As I said in Perl Review (4.3, p. 28):

I must show that I can use Turing-complete Perl code to determine the prototype of the dunno subroutine at compile time. A function definition won’t work.

Summarizing from that article, there are at least two ways that the prototype of a subroutine can be established using Turing-complete Perl code. One is with symbol table manipulation, for example:

BEGIN { *dunno = sub () { 3 } }

A second way is to put the function definition into a string which is eval'd in a BEGIN block. I believe clever monks will be able to think of others.

When putting a smiley right before a closing parenthesis, do you:

Use two parentheses: (Like this: :) )
Use one parenthesis: (Like this: :)
Reverse direction of the smiley: (Like this: (: )
Use angle/square brackets instead of parentheses
Use C-style commenting to set the smiley off from the closing parenthesis
Make the smiley a dunce: (:>
I disapprove of emoticons
Other